08/11/2022, 03:05 AM
I'd also like to add why the beta method doesn't solve this problem instantly. The beta method allows us to make:
\[
f^{\circ t}(z) : \mathbb{R} \times \mathbb{R} \to \mathbb{R}\cup\{\infty\}\\
\]
But, it produces a fibonacci solution \(\phi(t)\) which has poles all over the place. The theory of "producing the crescent iteration using the beta method" would be to some how use the beta solutions to create an entire \(\phi(t)\) as above. Which is unique, considering what we are asking of \(\theta^+\) and \(\theta^-\).
A lot to unpack here, I'm just trying to be as straight forward as possible.
\[
f^{\circ t}(z) : \mathbb{R} \times \mathbb{R} \to \mathbb{R}\cup\{\infty\}\\
\]
But, it produces a fibonacci solution \(\phi(t)\) which has poles all over the place. The theory of "producing the crescent iteration using the beta method" would be to some how use the beta solutions to create an entire \(\phi(t)\) as above. Which is unique, considering what we are asking of \(\theta^+\) and \(\theta^-\).
A lot to unpack here, I'm just trying to be as straight forward as possible.